In a collision of sufficient force, automobile air bags respond by electrically triggering the explosive decomposition of sodium azide \(\left(\mathrm{NaN}_{3}\right)\) to its elements. A \(50.0-\mathrm{g}\) sample of sodium azide was decomposed, and the nitrogen gas generated was collected over water at \(26^{\circ} \mathrm{C}\). The total pressure was \(745.5 \mathrm{mmHg}\). How many liters of dry \(\mathrm{N}_{2}\) were generated?

Chemical reactions are processes where substances, called reactants, are transformed into different substances, known as products. In the case of sodium azide (\text{NaN}_3), the substance decomposes into sodium (Na) and nitrogen gas (N_2) under certain conditions.

The balanced chemical equation for this decomposition is:

\[2NaN_3(s) \rightarrow 2Na(s) + 3N_2(g) \]

This equation indicates that 2 moles of sodium azide produce 3 moles of nitrogen gas. Balancing is crucial in chemical equations because it ensures that matter is conserved in the reaction. Each element must have the same number of atoms on both sides of the equation.

The ideal gas law is a mathematical relationship that describes the behavior of ideal gases. It is expressed as:

\[ PV = nRT \]

where \(P\) is the pressure, \(V\) is the volume, \(n\) is the number of moles, \(R\) is the ideal gas constant (0.0821 L atm/K mol), and \(T\) is the temperature in Kelvin. This equation allows us to calculate any one of these variables, provided we know the other three.

In our exercise, we used the ideal gas law to determine the volume of nitrogen gas produced. We needed to make sure we had the pressure in atmospheres and the temperature in Kelvin. By plugging in the values for moles of nitrogen gas, the temperature, and the corrected pressure, we could find the volume of nitrogen gas produced.

Stoichiometry involves using balanced chemical equations to calculate the quantities of reactants and products. It's essential for solving problems related to chemical reactions because it provides the ratios needed to convert between different substances.

In the decomposition of sodium azide, we needed to calculate the moles of nitrogen gas (\text{N}_2) produced knowing the amount of sodium azide (\text{NaN}_3) decomposed. Using the balanced equation:

\[2NaN_3(s) \rightarrow 2Na(s) + 3N_2(g) \]

we see that 2 moles of \text{NaN}_3 produce 3 moles of \text{N}_2. By calculating the moles of \text{NaN}_3 from its mass, and then using the ratio from the balanced equation, we determined how many moles of \text{N}_2 were produced.

When collecting gases over water, the measured pressure includes both the gas's pressure and the vapor pressure of water. This total pressure must be corrected to find the actual pressure of the gas alone.

In the problem, the total pressure (745.5 mmHg) includes the pressure of nitrogen gas and the vapor pressure of water at 26°C (25.2 mmHg). The pressure of nitrogen (\text{P}_{N_2}) is calculated by subtracting the water vapor pressure from the total pressure:

\[P_{N_2} = P_{total} - P_{water} \]

This correction ensures accurate calculations since the ideal gas law requires the pressure of the gas alone. After correction and converting to the appropriate units (atmospheres), we could then use this pressure in the ideal gas law to find the volume of the nitrogen gas.